Well, one show comes to mind. I started watching the first episode of Log Horizon, and found it to be too derivative of SAO at the time and skipped it. Little did we know that Isekai would become its own genre in anime, right? But then I went back and began re-watching it a few months later, and got really hooked. It was actually well done.

I would have to say Puella Magi Madoka Magica. While I did like the more realistic and mature take on magical girls the shiow wasn't hit any beats with me in the begging episodes. Until the darker stuff kicked in in the later episodes. Girls with guns, death is an actual and permit thing, and the cute mascot that doesn't do anything is the greatest master manipulator and villain. By the end I really enjoyed the series.

Steins;Gate. Steins;Gate had a strong beginning, but then slowed down almost immediately. I seriously considered dropping 5 episodes in. It growing on me would be an understatement because after a certain episode, it basically exploded in me. Steins;Gate is easily my favorite anime.

Baccano! is another one that comes to mind. The unconventional story telling threw me off at the beginning, but as the scrambled pieces started to form a coherent picture, it grew on me bit by bit. One of the few shows that I prefer dubbed.

Chuunibyou is one that took a while for me to appreciate. I actually dropped it at least 3 times. I don't really like slice of life and romance shows that progress as fast as a snail on a treadmill, but the memes had me coming back until I finished it. I liked it for what it is. Also it was cute af.

The last one is Gintama. This's an easy one. The watched anime I watched, the more references I got.